Tidal turbine array optimisation using the adjoint approach
Tidal turbine array optimisation using the adjoint approach
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DOI：
10.1016/j.renene.2013.09.031
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
S. Funke;P. Farrell;M. Piggott
中科院分区：
文献类型：
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作者：
S. Funke;P. Farrell;M. Piggott
海洋潮汐有可能产生大量的可再生能源。潮汐流发电机是提取和利用这一潜力的关键技术之一。为了提取经济上有用的电力量，通常必须将数百个潮汐涡轮机部署成阵列。这自然导致了这些涡轮机应该如何配置以提取最大可能功率的问题：涡轮机的定位和单独调谐可以显著影响提取的功率，因此具有重大的经济利益。然而，由于法律的场地限制、涡轮机尾流的非线性相互作用以及功率对流速的立方依赖性，手动优化是困难的。本文的新贡献是制定这个问题的物理模型，然后使用一个有效的基于梯度的优化算法解决的约束优化问题。在每次优化迭代中，二维有限元浅水模型预测当前阵列配置的流量和性能。然后，通过求解相关的伴随方程，在流解所花费的时间的一小部分中计算相对于涡轮机位置及其调谐参数提取的功率的梯度。这些方程通过计算向后传播因果关系，从提取的功率返回到涡轮机位置和调谐参数。这以几乎与涡轮机数量无关的成本产生梯度，这对于任何实际应用都是至关重要的。该方法的效用是通过优化涡轮机阵列在四个理想化的情况下，一个更现实的情况下，多达256涡轮机在内部声音的彭特兰湾，苏格兰。
Oceanic tides have the potential to yield a vast amount of renewable energy. Tidal stream generators are one of the key technologies for extracting and harnessing this potential. In order to extract an economically useful amount of power, hundreds of tidal turbines must typically be deployed in an array. This naturally leads to the question of how these turbines should be configured to extract the maximum possible power: the positioning and the individual tuning of the turbines could significantly influence the extracted power, and hence is of major economic interest. However, manual optimisation is difficult due to legal site constraints, nonlinear interactions of the turbine wakes, and the cubic dependence of the power on the flow speed. The novel contribution of this paper is the formulation of this problem as an optimisation problem constrained by a physical model, which is then solved using an efficient gradient-based optimisation algorithm. In each optimisation iteration, a two-dimensional finite element shallow water model predicts the flow and the performance of the current array configuration. The gradient of the power extracted with respect to the turbine positions and their tuning parameters is then computed in a fraction of the time taken for a flow solution by solving the associated adjoint equations. These equations propagate causality backwards through the computation, from the power extracted back to the turbine positions and the tuning parameters. This yields the gradient at a cost almost independent of the number of turbines, which is crucial for any practical application. The utility of the approach is demonstrated by optimising turbine arrays in four idealised scenarios and a more realistic case with up to 256 turbines in the Inner Sound of the Pentland Firth, Scotland.